Singular Value Decomposition (SVD) is a decomposition (factorization) of rectangular real or complex matrix into the product of a unitary rotation matrix, a diagonal scaling matrix, and a second unitary rotation matrix.
Questions tagged [svd]
84 questions
7
votes
1 answer
What is the fastest way to compute the sum of the singular values of a matrix?
Is there a faster way to compute the nuclear norm (trace norm, sum of singular values) of a matrix A than computing SVD(A) directly (or diagonalizing A^*A)?
I am particularly interested in the case where A is square. Assuming that A is real would…
Brent
- 171
- 4
3
votes
1 answer
Singular vectors of s1 for tiny dense matrices
I have a function whose main bottleneck is finding a(ny) singular vector pair in the space of the largest singular value, along with the singular value itself. This is done a huge number of times. This is the structure I know about:
Tiny. 4x4 is…
Ian Hincks
- 241
- 1
- 5
3
votes
1 answer
singular value decomposition of a 2 x 2 complex matrix
This should be easy, but...
I would like to express the singular value decomposition of a 2 x 2 complex matrix $A$ as function of its coefficients $A_{ij}$. In "closed form", no intermediate values, straight up.
What I mean is that if I express the…
Ali K
- 31
- 1
1
vote
0 answers
Computation of SVD of well-conditioned matrix takes more time than ill-conditioned matrix
I'm testing libraries for numerical computing and time they take to calculate SVD. During testing I encountered an issue for which I don't have an answer.
I generated 2 matrices:
random tall matrix using Matlab with function…
Intech
- 11
- 2